Most of Andreas Werckmeister's sources can be identified easily. This is not the case
with regard to his irregular circular tunings. It seems, however, that he was inspired by
two sources. The first one is Musica mathematica of Abraham Bartolus, published at
Leipzig in 1614. Bartolus takes over a tuning designed by Andreas Reinhard, published in
his Monochordum (Leipzig, 1604): the phrygian scale is divided into 48 parts and
related to the proportions of the universe. Bartolus praises this tuning: it would be
possible to make music in all keys. Werckmeister sees that the tuning needs to be tempered
first. The second source is a disc made by Theophil Staden, studied by Werckmeister in
Harsdörffers Mathematische und Philosophische Erquickstunden. It visualises
the idea of a circulair tuning in a primitive way.

Werckmeister's tunings known as Werckmeister III and Werckmeister IV are irrigular
circular. He recommended these tunings in particular, and not equal temperament, which is
regular circular, because he preferred the thirds to be purer, because the popular
meantone temperament was more related to Werckmeister III en IV, and possibly because
equal temperament was hard to realize accurately.